Average sampling and reconstruction in a reproducing kernel subspace of homogeneous type space

摘要

In this paper, we first introduce a reproducing kernel subspace of L~p(X, ρ,μ), where (X, ρ,μ) is a homogeneous type space. Then we consider average sampling and reconstruction of signals in the reproducing kernel subspace of L~p(X, ρ,μ), 1 ≤ p ≤∞.We show that signals in the reproducing kernel subspace of L~p(X, ρ,μ) could be stably reconstructed from its average samples taken on a relatively-separated set with small gap. Exponential convergence is established for the iterative approximation-projection reconstruction algorithm.